Question

Помогите пожалуйста с алгеброй. 7 класс. Тема: Пропорциональное деление. В сплав входят медь, олово и сурьма в отношении 4:15:6. Сколько процентов сплава составляет каждый металл? Какова масса этого сплава, если в нём меди меньше, чем олова, на 880 г?

Answer 1

4x+15x+6x=100
25x=100
x=4
16%, 60% и 24% соответсвенно.
60%-16%=44%
0.44x=880 (x-масса сплава)
x=2000гр или 2кг

Answer 2

Proportional Division of Alloy Components

To find the percentage of each metal in the alloy, we can use the concept of proportional division. The given ratio of copper (медь), tin (олово), and antimony (сурьма) in the alloy is 4:15:6.

Let's calculate the percentage of each metal in the alloy.

1. Copper (медь): - The given ratio states that for every 4 parts of the alloy, 1 part is copper. - To find the percentage, we divide the number of parts of copper by the total number of parts in the ratio and multiply by 100. - Percentage of copper = (4 / (4 + 15 + 6)) * 100

2. Tin (олово): - The given ratio states that for every 15 parts of the alloy, 1 part is tin. - To find the percentage, we divide the number of parts of tin by the total number of parts in the ratio and multiply by 100. - Percentage of tin = (15 / (4 + 15 + 6)) * 100

3. Antimony (сурьма): - The given ratio states that for every 6 parts of the alloy, 1 part is antimony. - To find the percentage, we divide the number of parts of antimony by the total number of parts in the ratio and multiply by 100. - Percentage of antimony = (6 / (4 + 15 + 6)) * 100

Let's calculate the percentages using the given ratio.

Calculation:

1. Percentage of copper: - Percentage of copper = (4 / (4 + 15 + 6)) * 100 - Percentage of copper = (4 / 25) * 100 - Percentage of copper = 16%

2. Percentage of tin: - Percentage of tin = (15 / (4 + 15 + 6)) * 100 - Percentage of tin = (15 / 25) * 100 - Percentage of tin = 60%

3. Percentage of antimony: - Percentage of antimony = (6 / (4 + 15 + 6)) * 100 - Percentage of antimony = (6 / 25) * 100 - Percentage of antimony = 24%

Therefore, the alloy consists of 16% copper, 60% tin, and 24% antimony.

Calculation of Alloy Mass:

To calculate the mass of the alloy, we need to know the mass of each metal in the alloy. The problem states that there is 880g more copper than tin in the alloy.

Let's assume the mass of tin in the alloy is x grams. Therefore, the mass of copper in the alloy would be (x + 880) grams.

Using the given ratio, we can set up the following equation:

(x + 880) / x = 4 / 15

Let's solve this equation to find the mass of tin in the alloy.

Calculation:

1. Cross-multiply the equation: - 15(x + 880) = 4x

2. Expand the equation: - 15x + 13200 = 4x

3. Simplify the equation: - 15x - 4x = -13200 - 11x = -13200

4. Solve for x: - x = -13200 / 11 - x ≈ -1200

Since the mass cannot be negative, we discard the negative solution.

Therefore, the mass of tin in the alloy is approximately 1200 grams.

To find the total mass of the alloy, we can add the mass of copper and tin:

Total mass of the alloy = Mass of copper + Mass of tin Total mass of the alloy = (x + 880) + x Total mass of the alloy = 2x + 880

Substituting the value of x, we can calculate the total mass of the alloy.

Calculation:

Total mass of the alloy = 2x + 880 Total mass of the alloy = 2 * 1200 + 880 Total mass of the alloy = 2400 + 880 Total mass of the alloy = 3280 grams

Therefore, the mass of the alloy is 3280 grams.

Please note that the negative solution for x was discarded as it does not make physical sense in this context.